Some fixed point theorems on non-convex sets

Mohanasundaram Radhakrishnan, S. Rajesh, Sushama Agrawal

Abstract

In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$

Keywords

fixed points; nonexpansive mappings; $T-$regular set; $k-$uniform convex Banach spaces; Opial property.

Subject classification

47H09; 47H10.

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References

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